Probability Theory in Gaming: Bernoulli Trials & Expected Values
From deciding who takes the first turn to resolving critical hits in tabletop RPGs, dice rolls and coin flips model fundamental statistical probability distributions.
Expected Values and Standard Normal Distribution in Multi-Dice Rolls
While rolling a single 6-sided die produces a uniform distribution (each number has a 16.67% chance), rolling multiple dice creates a bell curve (binomial distribution). The expected average roll of a standard D6 is $E[X] = 3.5$, whereas rolling 2D6 peaks at 7 (16.67% probability).
Frequently Asked Questions
Yes. Physical coins can have a microscopic bias (50.8% landing on the starting face due to center of mass asymmetry), but digital cryptographic coin flips are strictly 50.00% fair.
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